Methods to generate state space models by closed forms and transfer functions by recursive algorithms for RC interconnect and transmission line and their model reduction and simulations

Abstract

There is provided a set of methods with the exact accuracy to effectively calculate the n-th order state space models of RC distributed interconnect and transmission line in closed forms in time domain and transfer functions by recursive algorithms in frequency domain, where their RC components can be evenly distributed or variously valued. The main features include simplicity and accuracy of the said closed forms of the state space models {A,B,C,D} without involving matrix inverse and matrix multiplication operations, effectiveness and accuracy of the said recursive algorithms of the transfer functions, dramatic reduction of the calculation complexity to O(n) for the state space models, simulation methodology, and practice of various model reductions and their optimization. For evenly distributed RC interconnect and transmission line, the said closed form of state space model has its computation complexity of only a fixed constant, i.e., O(1).

Description

[0001]This application claims the benefit of U.S. Provisional Application No. 60 / 537,406 filed Jan. 20, 2004, and entitled as the above.STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT[0002]This invention was made with Government support under the NSF CCR 0098275 awarded by the National Science Foundation. The Government has certain rights in this invention.CROSS-REFERENCE TO RELATED APPLICATIONS[0003]No Related Nonprovisional ApplicationREFERENCE TO SEQUENCE LISTING, A TABLE, OR A COMPUTER PROGRAM LISTING COMPACT DISK APPENDIX[0004]Not ApplicableBACKGROUND OF THE INVENTION[0005]1. Field of the Invention[0006]The present invention relates to RC interconnect and transmission line, and methods to obtain their state space model in time domain and transfer function in frequency domain, and their simulations for their characteristics and evolution, and their practice for various model reduction methods.[0007]2. Description of the Related Art[0008]Over times, VLSI has becom...

AI Technical Summary

Benefits of technology

[0027]In light of the above, it will be apparent that a need exists in the art for RC interconnect and transmission line circuit model and its analysis method and system which can accurately capture the original model and the transient responses at all nodes in a computationally efficient manner.

[0032]It is yet another object of the invention to provide such a method and system of the model reduction having a high degree of stability in terms of both numerical stability and pole stability and physical synthesizable.

[0033]In short, it is a key objective of this present invention to provide exact accurate n-th order models and their simple algorithms of RC interconnect and transmission line by the said closed form of the state space model in time domain and the said recursive algorithm of the transfer function model in frequency domain. The main features include the exact accuracy of the models and high efficiency of the algorithms.

[0034]To achieve the above and other objects, the present invention is directed to a method and system for establishing the exact accuracy original models of the RC interconnect and transmission line in both time domain and frequency domain in a computationally efficient way (O(n) complexity, i.e., linear with n). For evenly distributed RC interconnect and transmission line, the said closed form of state space model has its computation complexity of only a fixed constant, i.e., O(1). The present invention also has guaranteed stability properties for low order approximations as compared to AWE, which can be a useful feature with RC interconnect and transmission lines which do not require high order approximations.

[0066]The corresponding time domain analysis and frequency domain analysis can be easily executed by the derived state space closed-form formulas and transfer functions such as by function command step and bode in MATLAB.

Problems solved by technology

With the rapid increase of integration level and speed, IC interconnect becomes one of the important limiting factors of today's VLSI circuit design performance.

With the continuous scaling of technology and increased die area, especially the chip operation speed increasing, that situation is becoming worse.

The increasing size of integrated systems creates an explosion in interconnect modeling complexity of unmanageable proportions.

As the interconnect complexity gradually increases, its electrical design becomes more challenging.

It is noticed that to get an accurate state space model for the starting point has significantly high computational complexity as shown as follows, in addition to the high computation complexity of model reduction techniques themselves.

For very high order system, the matrix inverse calculation leads to calculation singularity problem due to bad condition number of the matrix, making a calculation problem.

It is noticed that the limited number of orders or poles is inappropriate to evaluate the transient response at the nodes of underdamped RLC interconnect and transmission line, which require a much higher order model to accurately capture the transient response.

However, due to very large size of the original interconnect model, an important and difficult aspect is how to have a method to get its original model in a suitable time and cost-less calculation time.

However, it is only an approximation to exact transfer function due to no consideration of load effect or under an assumption of no load effect.

Thus, this fact implies that all one step back recursive algorithms are either not correct for an exact transfer function derivation if no load effect adjustment, or not efficient in computation complexity for derivation of the exact transfer function.

In all, current conventional methods are lack of an elegant way to get exact original high order state space model and effective recursive transfer function of distributed interconnect and transmission line.

Images